On-line radial basis function network center adaptation for nonlinear adaptive identification and control

Nonlinear adaptive identification and control are difficult to solve problems which are now being solved by the application of neural networks. Neural networks provide a solid framework for attacking these problems as they are described by adjustable parameters which are readily adaptable on-line and they are universal function approximators. Radial basis function networks have been shown to be functional in these systems especially when one attempts to consider the analytical proof of stability. Most algorithms developed for radial basis function networks for these applications consider only on-line adaptation of the output layer weights alone. This dissertation describes and demonstrates two novel algorithms which adapt the radial basis function center parameters as well as the output layer weights on-line. The first algorithm simply translates the initially chosen center lattice within the network input space. This algorithm is also shown to be equivalent to a recurrent radial basis function network. Using this algorithm results in faster learning of the output layer weights. The second algorithm described is a discrete-time algorithm that moves the centers to new locations within the network input space. Use of this algorithm reduces the amount of required a priori information about the functions to be approximated. Heuristic and analytical stability results are provided along with simulation examples which show the potential for these algorithms.